基于非线性映射的Fisher判别分析

提出一种非线性分类3-法——基于非线性映射的Fisher判别分析（NM-FDA）．首先提取基向量；然后采用Nystrom方法，以基向量为训练样本．将形式未知的非线性映射近似表达为已知形式的非线性映射，这种近似的非线性映射将变量由非线性的输入空间转换到线性的特征子空澡；最后对映射数据进行线性Fisher判别分析．实验采用7组标准数据集，结果显示NM-FDA具有较强的分类能力．     

A reformative kernel Fisher discriminant analysis

A reformative kernel Fisher discriminant method is proposed, which is directly derived from the naive kernel Fisher discriminant analysis with superiority in classification efficiency. In the novel method only a part of training patterns, called “significant nodes”, are necessary to be adopted in classifying one test pattern. A recursive algorithm for selecting “significant nodes”, which is the key of the novel method, is presented in detail. The experiment on benchmarks shows that the novel method is effective and much efficient in classifying.     

An efficient renovation on kernel Fisher discriminant analysis and face recognition experiments

A reformative kernel algorithm, which can deal with two-class problems as well as those with more than two classes, on Fisher discriminant analysis is proposed. In the novel algorithm the supposition that in feature space discriminant vector can be approximated by some linear combination of a part of training samples, called “significant nodes”, is made. If the “significant nodes” are found out, the novel algorithm on kernel Fisher discriminant analysis will be superior to the naive one in classification efficiency. In this paper, a recursive algorithm for selecting “significant nodes”, is developed in detail. Experiments show that the novel algorithm is effective and much efficient in classifying.     

Fast kernel Fisher discriminant analysis via approximating the kernel principal component analysis

Kernel Fisher discriminant analysis (KFDA) extracts a nonlinear feature from a sample by calculating as many kernel functions as the training samples. Thus, its computational efficiency is inversely proportional to the size of the training sample set. In this paper we propose a more approach to efficient nonlinear feature extraction, FKFDA (fast KFDA). This FKFDA consists of two parts. First, we select a portion of training samples based on two criteria produced by approximating the kernel principal component analysis (AKPCA) in the kernel feature space. Then, referring to the selected training samples as nodes, we formulate FKFDA to improve the efficiency of nonlinear feature extraction. In FKFDA, the discriminant vectors are expressed as linear combinations of nodes in the kernel feature space, and the extraction of a feature from a sample only requires calculating as many kernel functions as the nodes. Therefore, the proposed FKFDA has a much faster feature extraction procedure compared with the naive kernel-based methods. Experimental results on face recognition and benchmark datasets classification suggest that the proposed FKFDA can generate well classified features.     

一种基于空间变换的核Fisher鉴别分析

引入空间变换的思相想，提出了一种基于空间变换的核Fisher鉴别分析，与KFDA不同的是，该方法只需在一个较低维的空间内执行，从而较大幅度地降低了求解最优鉴别矢量集的计算量，提高了计算速度，在ORL标准人脸库上的试验结果验证了所提方法的有效性。     

Kernel direct discriminant analysis and its theoretical foundation

In this paper, the method of kernel direct discriminant analysis is analyzed from a new viewpoint and its theoretical foundation is revealed. Based on this result, an efficient and robust method is proposed. That is, the QR decomposition on the small-size matrix is adopted and then a small eigenvalue problem is solved. Finally, experimental results on ORL face database show that the proposed method is effective and feasible.     

Kernel clustering-based discriminant analysis

In this paper, a kernelized version of clustering-based discriminant analysis is proposed that we name KCDA. The main idea is to first map the original data into another high-dimensional space, and then to perform clustering-based discriminant analysis in the feature space. Kernel fuzzy c-means algorithm is used to do clustering for each class. A group of tests on two UCI standard benchmarks have been carried out that prove our proposed method is very promising.     

Variable selection in kernel Fisher discriminant analysis by means of recursive feature elimination

Variable selection serves a dual purpose in statistical classification problems: it enables one to identify the input variables which separate the groups well, and a classification rule based on these variables frequently has a lower error rate than the rule based on all the input variables. Kernel Fisher discriminant analysis (KFDA) is a recently proposed powerful classification procedure, frequently applied in cases characterised by large numbers of input variables. The important problem of eliminating redundant input variables before implementing KFDA is addressed in this paper. A backward elimination approach is recommended, and two criteria which can be used for recursive elimination of input variables are proposed and investigated. Their performance is evaluated on several data sets and in a simulation study.     

局部Fisher判别分析算法及仿真研究*

复杂化工过程常被多种类型的故障损坏,正常的训练数据无法建立准确的操作模型。为了提高复杂化工过程中故障的检测和分类能力,传统无监督Fisher判别分析(Fisher Discriminant Analysis,FDA)算法无法在多模态故障数据中的应用,本文提出基于局部Fisher判别分析(Local Fisher Discriminant Analysis,LFDA)的故障诊断方法。首先计算训练数据的局部类内和类间离散度矩阵,寻找LFDA的投影方向;其次把训练数据和测试数据向投影向量上投影,提取特征向量;最后计算特征向量间的欧氏距离,运用KNN分类器进行分类。把提出的LFDA方法应用到Tennessee Eastman(TE)过程,监控结果表明,LFDA的效果好于FDA和核Fisher判别分析(Kernel Fisher Discriminant Analysis,KFDA),说明LFDA方法在分类及检测不同类的故障方面具有高准确性及高灵敏度的优势。     

基于核空间距离测度的特征选择

提出核空间距离测度这一可分性判据。在核空间中计算两类样本点之间的距离,并以距离的大小评价子集的分类性能。使用顺序前进法作为搜索算法,在人造和真实的数据集上进行测试,文中的核空间距离测度可分性判据明显优于传统非核的可分性判据,优于或接近于Wang提出的核散布矩阵测度,并在运行时间上快一个数量级。将文中方法应用于胰腺内镜超声图像分类,取得较好分类结果。     

稀疏局部Fisher判别分析

提出一种稀疏局部Fisher判别分析（Sparsity Local Fisher Discriminant Analysis,SLFDA）。该算法在局部Fisher判别分析降维的基础上,通过平衡参数引入稀疏保持投影,在投影降维过程中保持了数据的全局几何结构和局部近邻信息。在UCI数据集和YaleB人脸数据集上的实验表明,该算法融合局部Fisher判别分析和稀疏保持投影的优点;与现有的半监督局部Fisher判别分析降维算法相比,该算法提高了基于最短欧氏距离的分类算法的精度。     

基于特征间距的二次规划特征选取算法

本文提出一种基于特征间距的二次规划特征选取算法。首先,将特征在类内样本间和异类样本间的距离分别作为二次规划算法目标函数的二次项和一次项参数,用以搜索类内紧密、内间分离的分类特征;同时,通过对二次项和一次项的归一化来均衡特征在同类样本和异类样本之间的关系;然后,将二次规划算法优化后的最优解向量作为衡量特征对分类贡献的权重向量,再根据特征权重高低选取分类特征。特征选取方法在6个数据集中的特征选取实验结果表明了该方法的可行性和有效性。     

Essence of kernel Fisher discriminant: KPCA plus LDA

In this paper, the method of kernel Fisher discriminant (KFD) is analyzed and its nature is revealed, i.e., KFD is equivalent to kernel principal component analysis (KPCA) plus Fisher linear discriminant analysis (LDA). Based on this result, a more transparent KFD algorithm is proposed. That is, KPCA is first performed and then LDA is used for a second feature extraction in the KPCA-transformed space. Finally, the effectiveness of the proposed algorithm is verified using the CENPARMI handwritten numeral database.     

A novel method for Fisher discriminant analysis

A novel model for Fisher discriminant analysis is developed in this paper. In the new model, maximal Fisher criterion values of discriminant vectors and minimal statistical correlation between feature components extracted by discriminant vectors are simultaneously required. Then the model is transformed into an extreme value problem, in the form of an evaluation function. Based on the evaluation function, optimal discriminant vectors are worked out. Experiments show that the method presented in this paper is comparative to the winner between FSLDA and ULDA.     

Classification in the presence of class noise using a probabilistic Kernel Fisher method

In machine learning, class noise occurs frequently and deteriorates the classifier derived from the noisy data set. This paper presents two promising classifiers for this problem based on a probabilistic model proposed by Lawrence and Schölkopf (2001). The proposed algorithms are able to tolerate class noise, and extend the earlier work of Lawrence and Schölkopf in two ways. First, we present a novel incorporation of their probabilistic noise model in the Kernel Fisher discriminant; second, the distribution assumption previously made is relaxed in our work. The methods were investigated on simulated noisy data sets and a real world comparative genomic hybridization (CGH) data set. The results show that the proposed approaches substantially improve standard classifiers in noisy data sets, and achieve larger performance gain in non-Gaussian data sets and small size data sets.     

Fuzzy discriminant analysis with kernel methods

A novel fuzzy nonlinear classifier, called kernel fuzzy discriminant analysis (KFDA), is proposed to deal with linear non-separable problem. With kernel methods KFDA can perform efficient classification in kernel feature space. Through some nonlinear mapping the input data can be mapped implicitly into a high-dimensional kernel feature space where nonlinear pattern now appears linear. Different from fuzzy discriminant analysis (FDA) which is based on Euclidean distance, KFDA uses kernel-induced distance. Theoretical analysis and experimental results show that the proposed classifier compares favorably with FDA.     

On a theoretical comparison between the orthonormal discriminant vector method and discriminant analysis

The performance of the orthonormal discriminant vector (ODV) method is discussed in comparison with discriminant analysis. The ODV method produces the features which maximize the Fisher criterion subject to the orthonormality of features. In contrast with discriminant analysis, the ODV method has no limitation on the maximum number of features to be extracted. From a theoretical viewpoint, it is proved that the ODV method is more powerful than discriminant analysis in terms of the Fisher criterion. The theoretical conclusion is experimentally verified using two real data sets.     

小波核局部Fisher判别分析的高光谱遥感影像特征提取

为了提高高光谱遥感影像的分类精度,充分利用影像的光谱和局部信息,文中提出小波核局部Fisher判别分析的高光谱遥感影像特征提取方法.通过小波核函数将数据集从低维原始空间映射至高维特征空间,考虑到数据的局部信息,利用加权矩阵计算散度矩阵,对局部Fisher判别准则函数求解最优特征矩阵,使不同类别的样本在高维特征空间中的可分离性更佳.在2个公开高光谱数据集上的实验表明,文中方法的总体分类精度和Kappa系数都有所提高.     

Enhanced semi-supervised local Fisher discriminant analysis for face recognition

An improved manifold learning method, called enhanced semi-supervised local Fisher discriminant analysis (ESELF), for face recognition is proposed. Motivated by the fact that statistically uncorrelated and parameter-free are two desirable and promising characteristics for dimension reduction, a new difference-based optimization objective function with unlabeled samples has been designed. The proposed method preserves the manifold structure of labeled and unlabeled samples in addition to separating labeled samples in different classes from each other. The semi-supervised method has an analytic form of the globally optimal solution and it can be computed based on eigen decomposition. Experiments on synthetic data and AT&T, Yale and CMU PIE face databases are performed to test and evaluate the proposed algorithm. The experimental results and comparisons demonstrate the effectiveness of the proposed method.